To install hardwood stair railings, first stain or paint the railing as desired. If applicable, remove the original railing. Once dry, drill holes in the newel posts. Install the bottom most posts so they fit as close to the step as possible, and fasten them in place using lag bolts. Also, drill holes in the wall to accommodate the highest newel post. Install it similarly to the bottom posts, but use toggle bolts to attach it directly to the wall.
Measure the length needed for the railing. Factor in the angle needed to match the slope of the stairs. Cut the railing appropriately.
Drill holes for the balusters through both the landing and treads. Use a specific drill bit designed to first make the hole, and then imprint a thread for the baluster's bolts to grip. Once the holes are drilled, insert the bolts. Place the balusters on top, and screw them flush against the stairs.
Secure the railing to the newel posts. Attach each baluster to the pre-drilled holes in the bottom of the railing. Attaching the angled part of the railing, as well as many of the balusters, may require loosening the bottom newel post. This portion of the job generally is easier to complete with more than one person. Once everything is aligned, re-fasten the newel post.